guess_recurrence

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations only declare readOnlyHint=true and openWorldHint=false, so the description carries the rest, and it does: it discloses the (r,d) search order by unknown count, the two-stage verification (mod a 61-bit prime, then exactly over Z), the `spare` over-determination requirement, and the caveat 'A guess, not a proof'. It even documents result fields (`spare_equations`, `integral`) that would otherwise be invisible since there is no output schema. Minor omissions are cost/runtime and failure behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The purpose is front-loaded in the first sentence before the procedural detail, and set notation is used economically. The paragraph is dense but each clause (input modes, search order, verification stages, result fields) carries distinct information, with little padding.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a genuinely complex search tool with 8 parameters and no output schema, the description supplies the algorithm, the input modes, and the meaning of two return fields, which is most of what an agent needs. The remaining gaps — which parameter caps order/degree/prediction count and how it relates to sibling tools — keep it short of complete.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 0% across 8 parameters, so the description must compensate. It explains `terms` (comma-separated, offset = n of first term), `anum`, `ext` (DATA + b-file terms), and `spare` (extra equations beyond unknowns) well, but `max_order`, `max_degree`, and `n_predict` are never named — only implicitly referenced via 'r', 'd', and 'predict further terms', leaving three of eight params ambiguous.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb (guess) and a precisely characterized resource (a P-recursive/holonomic recurrence with deg p_i <= d) plus the secondary action of predicting further terms. It is clear enough to distinguish from generic term-search tools, though it never names a sibling such as identify_transform or extend_from_formulas, so sibling differentiation is left implicit.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is implied rather than stated: it says to supply either `terms` with an offset or an `anum`, which tells the agent how to feed the tool but not when to prefer it over identify_transform or extend_from_formulas. There are no explicit when-not conditions or alternatives named, so the agent must infer placement.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.